Sensor devices having pressure sensors for measuring media pressures are prior art, see for example DE 102 12 767 A1. In particular, such prior art devices are used for monitoring the system pressure in systems that use pressurized fluids as working media. In an encapsulated system, the ambient pressure adds up to the system pressure, which gives rise to the difficulty that in the case of high ambient pressures. The pressure sensor must then be designed for a potentially very high pressure level. Even though a much lower system pressure relative to the ambient pressure is to be monitored only a small portion of the measurement range can then be used. For solving this problem according to the prior art, the sensor housing is brought to ambient pressure so that the pressure sensor is pressurized with the ambient pressure on the one hand and with the system pressure on the other hand. As a result, the sensor only measures the system pressure. In the case of sensor devices that are exposed to atmospheric pressure, the procedure is such that the pressure compensation between outside air and air present in the sensor housing is effected via a gas-permeable pressure compensation diaphragm. Such venting diaphragms are known as pressure compensation diaphragms, and they are commercially available in the form of hydrophobic-oleophobic PTFE diaphragms. For applications in which the sensor device is situated under water, this procedure is not feasible because air or nitrogen gas in the housing is compressible, and the diaphragm is not sufficiently supported. High differential pressures on the diaphragm then lead to water penetrating the housing and damaging the electronics associated with the sensor.